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9th grade · Math · Unit 17 of 17

Sequences

Arithmetic and geometric

What your child practices

Arithmetic and geometric sequences as functions: finding any term, writing a rule, and using a recursive rule.

Minnesota K-12 Academic Standards benchmark: 9.3.7.4 · arithmetic and geometric sequences

How we explain it

Children can open this short lesson before they practice.

  1. Arithmetic sequences add the same difference d.
  2. Term n = first term + (n − 1) × d.
  3. Geometric sequences multiply by the same ratio.

Example: What is term 10 of 4, 7, 10, 13, ...? d = 3. 4 + 9 × 3 = 31. Answer: 31

Sequences in Minnesota

In the Minnesota K-12 Academic Standards, this is unit 17 of 17 in 9th grade Math, after Two-Way Tables & Causation.

Gradelings describes a child's practice on this unit as Beginning, Approaching, Meeting or Exceeding (Four practice steps). That reflects practice, not a report-card mark: the teacher decides the mark.

Source: Minnesota Department of Education (MDE)

Sample questions

A taste of this unit. In the app, questions change every time and get easier or harder to match your child.

  1. Question 1

    Is 4, 6, 8, 10, ... arithmetic or geometric?

    • Arithmetic: add 2
    • Geometric: multiply by 2
    • Neither

  2. Question 2

    What is term number 17 of 4, 12, 20, 28, ...?

    answer box

  3. Question 3

    a(1) = 4 and a(n) = 2 × a(n − 1). What is a(5)?

    • 128
    • 64
    • 12
    • 40

  4. Question 4

    Which rule gives the sequence 5, 11, 17, 23, ... (n = 1, 2, 3, ...)?

    • a(n) = 7n − 2
    • a(n) = 6n − 1
    • a(n) = 5n + 6
    • a(n) = 6n + 5

  5. Question 5

    What is term number 20 of 1, −1, −3, −5, ...?

    answer box

  6. Question 6

    Is 2, 4, 6, 8, ... arithmetic or geometric?

    • Geometric: multiply by 2
    • Arithmetic: add 2
    • Neither

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